Ice flexural strength is an important parameter in the assessment of ice loads on the hulls of ice-class ships, sloped offshore structures, and sloped bridge piers. While scale effects in compressive ice strength are well known, there has been debate as to the extent of scale effects in ice flexural strength. To investigate scale effects during flexural failure of both freshwater and saline ice, a comprehensive up-to-date database of beam flexural strength measurements has been compiled. The database includes 2073 freshwater ice beam tests with beam volumes between 0.00016 and 2.197 m3, and 2843 sea ice beam tests with volumes between 0.00048 and 59.87 m3. The data show a considerable decrease in flexural strength as the specimen size increases, when examined over a large range of scales. Empirical models of freshwater ice flexural strength as a function of beam volume, and of saline ice as function of beam and brine volumes have been developed using regression analysis. For freshwater ice, the scale-dependent flexural strength is given as: σf=839(V/V1)0.13 For sea ice, the dependence of flexural strength has been modeled as: σ=1324(V/V1)0.054e4.969vb. Probabilistic models based on the empirical data were developed based on an analysis of the residuals, and can be used to enhance probabilistic analysis of ice loads where ice flexural strength is an input.

References

References
1.
Gudmestad
,
O.
,
Alhimenko
,
A.
, and
Løset
,
S.
,
2007
,
Engineering Aspects Related to Arctic Offshore Developments
, Student's Book for Institutes of Higher Education, LAN Publishing, St. Petersburg, Russia.
2.
Vaudrey
,
K. D.
,
1983
,
Characterization of Offshore and Coastal Ice Conditions
,
American Society of Civil Engineers
,
New York
.
3.
Timco
,
G. W.
, and
Weeks
,
W. F.
,
2010
, “
A Review of the Engineering Properties of Sea Ice
,”
Cold Regions Sci. Technol.
,
60
(
2
), pp.
107
129
.
4.
Borek
,
M.
,
Parsons
,
B. L.
, and
Hill
,
B.
,
1988
, “
Simple Beam Tests on Type S3 Sea Ice
,”
Seventh International Conference on Offshore Mechanics and Arctic Engineering
,
Houston, TX
,
Feb. 7–12
, pp.
63
68
.
5.
Weeks
,
W. F.
, and
Assur
,
A.
,
1967
,
Mechanical Properties of Sea Ice
,
Cold Regions Research and Engineering Laboratory
,
Hanover, NH
.
6.
Barrette
,
P.
,
Phillips
,
R.
, and
Clark
,
J.
,
1999
, “
Flexural Behavior of Model Sea Ice in a Centrifuge
,”
J. Cold Regions Eng.
,
13
(
3
), pp.
122
138
.
7.
Schwarz
,
J.
, and
Weeks
,
W. F.
,
1977
, “
Engineering Properties of Sea Ice
,”
J. Glaciol.
,
19
(
81
), pp.
499
531
.
8.
Weeks
,
W. F.
, and
Assur
,
A.
,
1969
,
Fracture of Lake and Sea Ice
,
U.S. Army Cold Regions Research and Engineering
,
Hanover, NH
.
9.
Frankenstein
,
G.
, and
Garner
,
R.
,
1970
,
Dynamic Young's Modulus and Flexural Strength of Sea Ice
,
U.S. Army Cold Regions Research and Engineering Laboratory
,
Hanover, NH
.
10.
Blanchet
,
D.
,
Abdelnour
,
R.
, and
Comfort
,
G.
,
1997
, “
Mechanical Properties of First-Year Sea Ice at Tarsiut Island
,”
J. Cold Regions Eng.
,
11
(
1
), pp.
59
83
.
11.
Tatinclaux
,
J. C.
, and
Wu
,
C. Y.
,
1978
, “
On Flexural Strength of Freshwater and Saline Ice
,”
Conference on Applied Techniques for Cold Environments
,
Anchorage, AK
,
May 17–19
, pp.
295
306
.
12.
Timco
,
G. W.
, and
O.'Brien
,
S.
,
1994
, “
Flexural Strength Equation for Sea Ice
,”
Cold Regions Sci. Technol.
,
22
(
3
), pp.
285
298
.
13.
Tozawa
,
S.
, and
Taguchi
,
Y.
,
1986
, “
A Preliminary Study of Scale Effect on Flexural Strength of Ice Specimen
,”
Fifth International Offshore Mechanics and Arctic Engineering Symposium, Tokyo, Japan, Apr. 13.
14.
Sanderson
,
T. J.
,
1988
,
Ice Mechanics and Risks to Offshore Structures
,
Kluwer Academic Publishers
,
Norwell, MA
.
15.
Batdorf
,
S.
, and
Heinisch
,
H.
, Jr
.,
1978
, “
Weakest Link Theory Reformulated for Arbitrary Fracture Criterion
,”
J. Am. Ceram. Soc.
,
61
(
7–8
), pp.
355
358
.
16.
Evans
,
A. G.
,
1978
, “
A General Approach for the Statistical Analysis of Multiaxial Fracture
,”
J. Am. Ceram. Soc.
,
61
(
7–8
), pp.
302
308
.
17.
Reid
,
S.
,
1991
, “
Flaws in the Failure Prediction Model of Glass Strength
,”
Sixth International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP6)
,
Mexico City
,
June 17–21
, pp.
111
117
.
18.
van Mier
,
J. G.
,
1997
,
Fracture Process of Concrete: Assessment of Material Parameters for Fracture Models
,
CRC Press
,
Boca Rotan, FL
.
19.
Taylor
,
R.
, and
Jordaan
,
I.
,
2015
, “
Probabilistic Fracture Mechanics Analysis of Spalling During Edge Indentation in Ice
,”
Eng. Fract. Mech.
,
134
, pp.
242
266
.
20.
Jordaan
,
I.
,
Taylor
,
R.
, and
Derradji-Aouat
,
A.
,
2012
, “
Scaling of Flexural and Compressive Ice Failure
,”
ASME
Paper No. OMAE2012-84033.
21.
Williams
,
F. M.
, and
Parsons
,
B. L.
,
1994
, “
Size Effect in the Flexural Strength of Ice
,” 13th International Conference on Offshore Mechanics and Arctic Engineering, Houston, TX, Feb. 27–Mar. 3
22.
Lau
,
M.
,
Phillips
,
R.
, and
McKenna
,
R.
,
2001
, “
Size Effect on the Flexural Strength of Ice in Model Testing
,”
16th International Conference on Port and Ocean Engineering Under Arctic Conditions
,
Ottawa, ON, Canada
,
Aug. 12–17
, pp.
1413
1421
.
23.
Lavrov
,
V. V.
,
1971
, “
Deformation and Strength of Ice [Deformatsiya i Prochnost' L' Da] (English)
,” National Technical Information Service, Springfield, VA, Report No.
SFCSINSF(TT7050130)
.https://trid.trb.org/view/1807
24.
Frederking
,
R.
, and
Sudom
,
D.
,
2013
, “
Review of Flexural Strength of Multi-Year Ice
,”
23th International Offshore and Polar Engineering Conference
, Anchorage, AK, June 30–July 5, pp. 1087–1093.https://www.onepetro.org/conference-paper/ISOPE-I-13-195
25.
Määttänen
,
M.
,
1975
, “
On the Flexural Strength of Brackish Water Ice by In-Situ Tests
,” POAC 1975 Conference, Fairbanks, AK, Aug. 11--15, pp.
349
359
.
26.
Parsons
,
B. L.
, and
Lal
,
M.
,
1991
, “
Distribution Parameters for Flexural Strength of Ice
,”
Cold Regions Sci. Technol.
,
19
(
3
), pp.
285
293
.
27.
Parsons
,
B. L.
,
Lal
,
M.
, and
Williams
,
F. M.
,
1992
, “
The Influence of Beam Size on the Flexural Strength of Sea Ice, Freshwater Ice and Iceberg Ice
,”
Philos. Mag. A
,
66
(
6
), pp.
1017
1036
.
28.
Frederking
,
R. M. W.
, and
Timco
,
G. W.
,
1983
, “
On Measuring Flexural Properties of Ice Using Cantilever Beams
,”
Ann. Glaciol.
,
4
, pp.
58
65
.
29.
Dempsey
,
J. P.
,
Nigam
,
D.
, and
Cole
,
D. M.
,
1988
, “
The Flexure and Fracture of Macrocrystalline S1 Type Freshwater Ice
,”
Seventh International Conference on Offshore Mechanics and Arctic Engineering
,
Houston, TX
,
Feb. 7–12
, pp.
39
46
.
30.
Barrette
,
P. D.
,
2011
, “
A Laboratory Study on the Flexural Strength of White Ice and Clear Ice From the Rideau Canal Skateway
,”
Can. J. Civ. Eng.
,
38
(
12
), pp.
1435
1439
.http://www.nrcresearchpress.com/doi/pdf/10.1139/l11-106
31.
Tabata
,
T.
,
1967
, “
Studies of the Mechanical Properties of Sea Ice X: The Flexural Strength of Small Sea Ice Beams
,”
International Conference on Low Temp Science; Physics of Snow and Ice
,
Sapporo, Japan
,
Aug. 14–19
, pp.
481
497
.
32.
Frankenstein
,
G. E.
,
1959
, “
Strength Data on Lake Ice
,”
U.S. Army Snow Ice and Permafrost Research Establishment
,
Corps of Engineers
,
Wilmette, IL
, p.
20
.
33.
Gow
,
A. J.
, and
Langston
,
D.
,
1975
, “
Flexural Strength of Lake Ice in Relation to Its Growth Structure and Thermal History
,” U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH, Report No.
CRREL-RR-349
.http://acwc.sdp.sirsi.net/client/en_US/default/index.assetbox.assetactionicon.view/1015140?rm=CCREL+RESEARCH0%7C%7C%7C1%7C%7C%7C1%7C%7C%7Ctrue
34.
Gow
,
A. J.
,
Ueda
,
H. T.
, and
Ricard
,
J. A.
,
1978
, “
Flexural Strength of Ice on Temperate Lakes Comparative Tests of Large Cantilever and Simply Supported Beams
,” U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH, Report No. CRREL-78-9.
35.
Gow
,
A. J.
,
Ueda
,
H. T.
, and
Govoni
,
J. W.
,
1988
, “
Temperature and Structure Dependence of the Flexural Strength and Modulus of Freshwater Model Ice
,” U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH, Report No.
CRREL-88-6
.https://apps.dtic.mil/dtic/tr/fulltext/u2/a199637.pdf
36.
Timco
,
G. W.
, and
Frederking
,
R. M. W.
,
1983
, “
Flexural Strength and Fracture Toughness of Sea Ice
,”
Cold Regions Sci. Technol.
,
8
(
1
), pp.
35
41
.
37.
Drouin
,
M.
, and
Michel
,
B.
,
1972
,
La Resistance en Flexion de la Glace du St-Laurent Détermiée en Nature
,
Laboratoire de Mécanique des Glaces, Département de Génie Civil, Faculté des Sciences, Université Laval
,
Quebec City, QC, Canada
.
38.
Williams
,
J. L.
,
1990
, “
Three Point Loading of Freshwater Ice Beams
,” National Research Council Canada, St. John's, NL, Canada, Report No. LM-1990-13.
39.
Murat
,
J. R.
, and
Tinwai
,
R.
,
1977
, “
Sea Ice Testing in Flexure
,”
International Conference on Port and Ocean Engineering Under Arctic Conditions (POAC 77)
, St. John's, NL, Canada, Sept. 26–30, pp.
638
653
.
40.
Ervik
,
Å.
,
2013
, “
Experimental and Numerical Investigations of Cantilever Beam Tests in Floating Ice Covers
,”
Master thesis
,
UNIS Publication Series, Lonyearbyen, Svalbard
.
41.
Lau
,
P.
, and
Browne
,
C.
,
1989
, “
Bending and Compression Properties of Young Sea Ice
,”
OCEANS'89
, Seattle, WA, Sept. 18–21, pp.
1292
1296
.
42.
Vaudrey
,
K.
,
1975
,
Ice Engineering: Elastic Property Studies on Compressive and Flexural Sea Ice Specimens
,
U.S. Naval Construction Battalion Center
,
Port Hueneme, CA
.
43.
Saeki
,
H.
,
Nomura
,
T.
, and
Ozaki
,
A.
,
1978
, “
Experimental Study on the Testing Methods of Strength and Mechanical Properties for Sea Ice
,”
Fourth IAHR Symposium on Ice
,
Lulea, Sweden
,
Aug. 7–9
, pp.
135
149
.
44.
Butkovich
,
T. R.
,
1956
, “
Strength Studies of Sea Ice
,”
Snow Ice and Permafrost Research Establishment
,
Corps of Engineers, U.S. Army
,
Wilmette, IL
.
45.
Butkovich
,
T. R.
,
1959
, “
On the Mechanical Properties of Sea Ice, Thule, Greenland, 1957
,” U.S. Army CRREL, Hanover, NH, Report No. 54.
46.
Frederking
,
R. M. W.
, and
Häusler
,
F. U.
,
1978
, “
Flexural Behaviour of Ice From In Situ Cantilever Beams Tests
,”
IAHR Symposium on Ice Problems
,
Luleå, Sweden
,
Aug. 7–9
, pp.
197
215
.
47.
Kayo
,
Y.
,
Kawasaki
,
T.
, and
Minami
,
T.
,
1983
, “
Field Study on Mechanical Strength of Sea Ice at East Coast of Hokkaido
,”
Seventh International Conference on Port and Ocean Engineering Under Arctic Conditions
,
Helsinki, Finland
,
Apr. 5–9
, pp.
109
118
.
48.
Lainey
,
L.
, and
Tinawi
,
R.
,
1981
, “
Parametric Studies of Sea Ice Beams Under Short and Long Term Loadings
,”
IAHR International Symposium on Ice
,
Quebec, QC, Canada
,
July 27–31
, pp.
607
619
.
49.
Michailidis
,
M.
,
1981
, “
M.V. Arctic Probe Into Lake Melville Labrador
,” Arctic Vessel and Marine Research Institute (AVMRI), Ottawa, ON, Canada, Report No. LTR-SH-322.
50.
Tabata
,
T.
,
Fujino
,
K.
, and
Aota
,
M.
,
1967
, “
Studies of the Mechanical Properties of Sea Ice XI: The Flexural Strength of Sea Ice In Situ
,”
International Conference on Low Temp Science; Physics of Snow and Ice,
Sapporo, Japan, Aug. 14–19, pp.
539
550
.https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/20323/1/1_p539-550.pdf
51.
Frederking
,
R. M. W.
,
Timco
,
G. W.
, and
Gulf
,
R. C.
,
1982
, “
NRC Ice Property Measurements at Tarsiut Island, Beaufort Sea, Winter 1981-82
,” National Research Council of Canada, Calgary, AB, Canada, Accession No. ASTI46224.
52.
Weeks
,
W. F.
, and
Anderson
,
D. L.
,
1958
, “
An Experimental Study of Strength of Young Sea Ice
,”
Am. Geophys. Union
,
39
(
4
), pp.
641
647
.
53.
Williams
,
F.
,
Spencer
,
D.
, and
Parsons
,
B.
,
1991
, “
Full-Scale Ice Breaker Trials CCGS Sir John Franklin Indian Arm/Little Burnt Bay 1991
,” National Research Council Canada, St. John's, NL, Canada, Technical Report No. TR-1991-03.
54.
Williams
,
F.
,
Everard
,
J.
, and
Butt
,
S.
,
1992
, “
Ice and Snow Measurements in Support of the Operational Evaluation of the Nathanial B. Palmer in the Antarctic Winter Environment
,” National Research Council Canada, St. John's, NL, Canada, Technical Report No. TR-1992-14.
55.
Williams
,
F.
,
Crocker
,
G.
, and
Butt
,
S.
,
1993
, “
Northumberland Strait Ice Properties Measurements
,” National Research Council, Institute for Marine Dynamic, St. John's, NL, Canada, Technical Report No. TR-1993-06.
56.
Williams
,
F. M.
,
Kirby
,
C.
, and
Slade
,
T.
,
1993
, “
Strength and Fracture Toughness of First Year Arctic Sea Ice NRC Institute for Ocean Technology,” National Research Council Canada
, St. John's, NL, Canada, Technical Report No. TR-1993-12.
57.
Airaksinen
,
K.
,
1974
, “
Free Beam Tests and Friction Tests at Pond Inlet, N.W.T.
,”
Polarforschung
,
44
(
1
), pp.
71
75
.https://epic.awi.de/id/eprint/28027/1/Polarforsch1974_1_9.pdf
58.
Saeki
,
H.
,
Ozaki
,
A.
, and
Kubo
,
Y.
,
1981
, “
Experimental Study on Flexural Strength and Elastic Modulus of Sea Ice
,”
Sixth International Conference on Port and Ocean Engineering Under Arctic Conditions
,
Quebec City, QC, Canada
,
July 27–31
, pp.
536
547
.
59.
Dykins
,
J.
,
1971
, “
Ice Engineering–Material Properties of Saline Ice for a Limited Range of Conditions
,” U.S. Naval Civil Engineering Laboratory, Port Hueneme, CA, Accession No. AD0887840.
60.
Marchenko
,
A.
,
Karulina
,
M.
, and
Karulin
,
E.
,
2017
, “
Flexural Strength of Ice Reconstructed From Field Tests With Cantilever Beams and Laboratory Tests With Beams and Disks
,”
International Conference on Port and Ocean Engineering Under Arctic Conditions
,
Busan, South Korea
,
June 11–16
, pp.
1
10
.
61.
Dykins
,
J.
,
1968
, “
Tensile and Flexural Properties of Saline Ice
,”
International Symposium on Physics of Ice
,
Munich, Germany
,
Sept. 9–14
, pp.
251
270
.
62.
Kujala
,
P.
,
Riska
,
K.
, and
Varsta
,
P.
,
1990
, “
Results From In Situ Four Point Bending Tests With Baltic Sea Ice
,”
IAHR Symposium on Ice Problems
,
Espoo, Finland
,
Aug. 20–23
, pp.
261
278
.
63.
Butkovich
,
T. R.
,
1959
,
Some Physical Properties of Ice From the TUTO Tunnel and Ramp, Thule, Greenland
, Vol.
47
,
U.S. Army CRREL
,
Hanover, NH
.
64.
Ji
,
S.
,
Wang
,
A.
, and
Su
,
J.
,
2011
, “
Experimental Studies on Elastic Modulus and Flexural Strength of Sea Ice in the Bohai Sea
,”
J. Cold Regions Eng.
,
25
(
4
), pp.
182
195
.
65.
Christensen
,
F.
,
1986
, “
Sea Ice Strength Measurements From the Inner Danish Waters in Early 1985
,”
First International Conference on Ice Technology
,
Cambridge, MA
, pp.
247
253
.
66.
Shapiro
,
L.
, and
Weeks
,
W.
,
1995
, “
Controls on the Flexural Strength of Small Plates and Beams of First-Year Sea Ice
,”
ASME Appl. Mech. Div.
,
207
, pp.
179
179
.
67.
Tatinclaux
,
J.
, and
Wu
,
C.
,
1976
, “
Laboratory Study of the Flexural Strength and Elastic Modulus of Freshwater and Saline Ice
,” Iowa Institute of Hydraulic Research, University of Iowa, Iowa City, IA, Report No. 190.
68.
Aly
,
M.
,
2018
, “
Analysis of Scale Effects in Ice Flexural Strength
,” Master's thesis, Memorial University of Newfoundland, St. John's, NL, Canada.
69.
Svec
,
O. J.
, and
Frederking
,
R.
,
1981
, “
Cantilever Beam Tests in an Ice Cover: Influence of Plate Effects at the Root
,”
Cold Regions Sci. Technol.
,
4
(
2
), pp.
93
101
.
70.
Svec
,
O. J.
,
Thompson
,
J.
, and
Frederking
,
R.
,
1985
, “
Stress Concentrations in the Root of an Ice Cover Cantilever: Model Tests and Theory
,”
Cold Regions Sci. Technol.
,
11
(
1
), pp.
63
73
.
72.
Weibull
,
W.
,
1951
, “
Wide Applicability
,”
ASME J. Appl. Mech.
,
103
(
730
), pp.
293
297
.https://pdfs.semanticscholar.org/88c3/7770028e7ed61180a34d6a837a9a4db3b264.pdf
73.
Gladwell
,
R.
,
1977
, “
Field Studies of the Strength and Physical Properties of a Multi-Year Ice Pressure Ridge in the Southern Beaufort Sea
,” Arctic Petroleum Operators' Association, Calgary, AB, Canada, Report by Imperial Oil Limited, Calgary, AB, Canada, Report No. 1.
74.
Schwarz
,
J.
,
Frederking
,
R.
, and
Gavrillo
,
V.
,
1981
, “
Standardized Testing Methods for Measuring Mechanical Properties of Ice
,”
Cold Regions Sci. Technol.
,
4
(
3
), pp.
245
253
.
75.
Frankenstein
,
G. E.
,
1966
,
Strength of Ice Sheets
,
U.S. Crrel
,
Hanover, NH
.
76.
Frankenstein
,
G.
, and
Garner
,
R.
,
1967
, “
Equations for Determining the Brine Volume of Sea Ice From −0.5° to −22.9 °C
,”
J. Glaciol.
,
6
(
48
), pp.
943
944
.
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